Geometrical picture of the electron-electron correlation at the large-D limit
arXiv:2111.13996 · doi:10.1039/D2CP00438K
Abstract
In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron-electron correlations and might give a bound on the correlation energy. The results at the large-D limit and at D=3 indicate the feasibility of using the geometrical picture to get a bound on the electron-electron correlations.
arXiv comment27 pages, 13 figures
References in corpus (34)
- Quantum entanglement
- The density-matrix renormalization group
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Scaling of Entanglement close to a Quantum Phase Transitions
- Entropy and Area
- Entanglement in a simple quantum phase transition
- Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
- Area laws in quantum systems: mutual information and correlations
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Observation of the Wigner-Huntington Transition to Solid Metallic Hydrogen
- Characterizing Entanglement
- Entanglement Properties of the Harmonic Chain
- Entropy, entanglement, and area: analytical results for harmonic lattice systems
- Site-resolved measurement of the spin-correlation function in the Hubbard model
- A symmetry principle for Topological Quantum Order
- Entanglement entropy in fermionic Laughlin states
- An entanglement-area law for general bosonic harmonic lattice systems
- Entropy and Entanglement in Quantum Ground States
- Observation of canted antiferromagnetism with ultracold fermions in an optical lattice
- Probing real-space and time resolved correlation functions with many-body Ramsey interferometry
- A First-order Phase Transition to Metallic Hydrogen
- An area law for entanglement from exponential decay of correlations
- Entanglement as Measure of Electron-Electron Correlation in Quantum Chemistry Calculations
- An area law for the entropy of low-energy states
- Energy as an Entanglement Witness for Quantum Many-Body Systems
- Entanglement Entropy beyond the Free Case
- Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices
- Ground states of unfrustrated spin Hamiltonians satisfy an area law
- Capturing static and dynamic correlation with -MP2 and -CCSD
- Dimensional interpolation for metallic hydrogen
- Dimensional Interpolation for Random Walk